about local correlation coefficient（LCC）

[cs123951]

Hi, I have read the paper "sotropic Total Variation Regularization of Displacements in Parametric Image Registration" carefully, especially the part of "Image Dissimilarity Metric". But your code is not corresponding to the formula (4)-(7) in your article. Maybe there are something you didn't write in the paper.
And I'm confused about the Fourier domain. Why do this carried out in the Fourier domain rather than image spatial domain?
I do not understand the following formula in "README.md",either.

Could you give some more explanations?
Thanks a lot.